Is there an example of a smooth projective variety over $\mathbb{C}$ where its easy to see that its integral cohomology has torsion?
Are there criteria for seeing that the integral cohomology does not have torsion? (For example, do smooth hypersurfaces have torsion in their cohomology?)
Edit: I just realized for hypersurfaces, we can use Lefschetz to show only the middle cohomology matters, and then apply universal coefficient theorem (torsion shifts up by one dimension from homology to cohomology) to see there isn't torsion. But I guess beyond Lefschetz, universal coefficient theorem, and poincare duality, I don't know any methods.